there is nothing special about reaching failure. what makes a muscle grow is time under tension and progressive overload. over working a muscle by pushing it to failue repeatedly only inhibits your bodies ability to grow as it has to deal with the damage caused by those sets. one set to failure is ok and can work but the idea is to get your muscle able to lift heavy weight for a bunch of sets in multiple rep ranges. whats going to be bigger, a muscle that can do one set to failure at 10 reps with 300lbs or a muscle that can do 10 easy sets of 6 with 300lbs. the muscle capable of doing multiple sets will be bigger than the one which can only do one set.
I agree with the concept of TUT being a far more accurate method than counting reps (though it is not practical). Your muscles don't count numbers but it does know (metaphorically speaking) how long it is under tension. If you do, say 8 reps on the bench without fully locking out your muscle are under constant tension during that set. If instead you lock out after each rep and pause for a second or so that is quite different. But TUT, in and of itself is not enough, it is a necessary but insufficient condition for stimulating an adaptive reponse. If I pick up a five pound dumbbell and curl it for five minutes I don't think it will stimulate an adaptive response in regard to stimulating size and strength, then if I took a 45 lb dumbbell and crank out 10 clean reps failing to get the 11th.
And you are quite right that "over working a muscle by pushing it to failue repeatedly only inhibits your bodies ability to grow as it has to deal with the damage caused by those sets."
The operative phrases here are "repeatedly" and "over working" which is the reason the training sessions are kept brief and allowing for sufficient recovery. And this varies from individual to individual, age, life styles, etc. To make a blanket statement that it takes x number of days for a muscle to grow and recover doesn't seem accurate. Even if you take identical twins, better yet clones, but all one does is lift weights and lays around all day and sleeps 10-12 hours a night as opposed to his unfortunate twin who works construction 12 hours a day in the hot sun and sleeps six hours a day. And this assumes that calories are NOT the same but that the more active individual consumes far more so that his caloric surplus matches his twin.
also, and this is a key point, just because your not pushing your muscle to the point of failure, does not mean the weight was easy to lift or that your muscle hasnt been taxed/stimulated. every single time you rep a weight you are stimulating growth. more reps without over training= more growth. the idea is to push yourself, lift heavy, do a mixture of rep ranges, keep good form, but not to tax your cns and muscle fibers to the point where they have to focus on repairing damage instead of growing.
This corresponds to your initial point that "there is nothing special about reaching failure." It is special in the sense that you are working more intensely than if you were to stop, say, two reps from failure. And, yes, it does not mean that the weight was easy to lift (though you could say "easier" of that your muscle "hasn't been taxed/stimulated." Mentzer addressed this possibility. Who is to say that it ONLY takes 100% momentary maximal effort? Maybe it's 95% or 90%? Maybe even just 70%? I think even you, yourself, suggested, 85%(?). But the problem is, how do you measure it? How do you know if you are working at 92% of your maximum effort? Mentzer propose that you can only accurately measure two values of intensity: Zero and a 100.
But unlike zero percent of intensity which I think can be measured exactly; 100% is still a subjective evaluation. There's 100% of effort and there's
100% of effort with Jones pointing a pistol at your head as he allegedly did to Viator. But it's still measured much more accurately than some midrange percent of intensity of effort.
And I don't think it make intuitive sense that every single time you rep a weight you are stimulating growth. In fact, this is disproved everywhere at every time at all gyms throughout the world. I've trained in a lot of different gym throughout my 39 years of continuous training and the vast majority of the trainees in there don't look like they've ever exercised a day in their life. Say, your best bench lift is 315 lbs for 8 reps. But instead you just do one to two reps every time you bench. Do you think you'll make any progress at all?
"the idea is to push yourself, lift heavy, do a mixture of rep ranges, keep good form"
Yes: intensity, progression, and varying the stimuli.